Final answer:
To determine the equation of a line perpendicular to AB, it's necessary to know the slope of AB, as perpendicular lines have slopes that are negative reciprocals. Without the slope of AB, we cannot confidently choose from the given options, since there's no way to determine the correct slope of the perpendicular line.
Step-by-step explanation:
To find the equation of a line perpendicular to line AB and passing through the point (1,2), we need to understand the concept of slopes of perpendicular lines. Lines that are perpendicular to each other have slopes that are negative reciprocals of each other. Unfortunately, the equation of line AB is not provided in the question, but we can still analyze the given options.
For two lines to be perpendicular, if one line has a slope m, the other line will have a slope of -1/m. This means if the slope of AB is given or can be deduced, we can calculate the slope of the line perpendicular to it and then find an equation that has this perpendicular slope and goes through the specified point.
Since we don't have the slope of AB, we can only guess that one of the choices given has the correct perpendicular slope. However, without knowing the slope of AB, we cannot definitively choose the correct option.
For illustration, if the slope of line AB were, for example, 2, we would be looking for an equation with a slope of -1/2 to be perpendicular to it. Given the point (1,2), we would substitute these values into the slope-intercept form equation, y = mx + b, and solve for b. However, without the slope of AB, we cannot solve this problem definitively.